Performance of the air2stream model that relates air and stream water temperatures depends on the calibration method

Abstract A number of physical or data-driven models have been proposed to evaluate stream water temperatures based on hydrological and meteorological observations. However, physical models require a large amount of information that is frequently unavailable, while data-based models ignore the physical processes. Recently the air2stream model has been proposed as an intermediate alternative that is based on physical heat budget processes, but it is so simplified that the model may be applied like data-driven ones. However, the price for simplicity is the need to calibrate eight parameters that, although have some physical meaning, cannot be measured or evaluated a priori. As a result, applicability and performance of the air2stream model for a particular stream relies on the efficiency of the calibration method. The original air2stream model uses an inefficient 20-year old approach called Particle Swarm Optimization with inertia weight. This study aims at finding an effective and robust calibration method for the air2stream model. Twelve different optimization algorithms are examined on six different streams from northern USA (states of Washington, Oregon and New York), Poland and Switzerland, located in both high mountains, hilly and lowland areas. It is found that the performance of the air2stream model depends significantly on the calibration method. Two algorithms lead to the best results for each considered stream. The air2stream model, calibrated with the chosen optimization methods, performs favorably against classical streamwater temperature models. The MATLAB code of the air2stream model and the chosen calibration procedure (CoBiDE) are available as Supplementary Material on the Journal of Hydrology web page.

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